Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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4
![**Evaluate**
\[ \lim_{(x,y) \to (3,1)} \frac{x^2 - 7xy + 12y^2}{x - 3y} \]
**Explanation:**
The task is to evaluate the limit of a function of two variables as \((x, y)\) approaches the point \((3, 1)\). The function given is a rational expression with a polynomial in both the numerator and the denominator.
- **Numerator:** \(x^2 - 7xy + 12y^2\)
- This is a quadratic polynomial in two variables.
- **Denominator:** \(x - 3y\)
- A linear expression in two variables.
The main challenge in evaluating this limit is dealing with potential indeterminate forms that occur when both the numerator and denominator approach zero at the same time. Techniques like factoring, simplifying, or using paths to evaluate may be necessary to determine the limit, if it exists.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf03a655-6476-4846-869e-21c3171bdd2c%2F45fb1ee3-e5bc-4f3c-8db0-ee735510289a%2F6py867c_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate**
\[ \lim_{(x,y) \to (3,1)} \frac{x^2 - 7xy + 12y^2}{x - 3y} \]
**Explanation:**
The task is to evaluate the limit of a function of two variables as \((x, y)\) approaches the point \((3, 1)\). The function given is a rational expression with a polynomial in both the numerator and the denominator.
- **Numerator:** \(x^2 - 7xy + 12y^2\)
- This is a quadratic polynomial in two variables.
- **Denominator:** \(x - 3y\)
- A linear expression in two variables.
The main challenge in evaluating this limit is dealing with potential indeterminate forms that occur when both the numerator and denominator approach zero at the same time. Techniques like factoring, simplifying, or using paths to evaluate may be necessary to determine the limit, if it exists.
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